Nota de FísicaPublicado
The Strong-Coupling Expansion and the Ultra-local Approximation in Scalar Theories
N.F. Svaiter
2003
Dados da publicação
- Autores
- N.F. Svaiter
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 2003
- Descrição
- We discuss the strong-coupling expansion in Euclidean field theory. In a formal representation for the Schwinger functional, we treat the off-diagonal terms of the Gaussian factor as a perturbation about the remaining terms of the functional integral. Consequently, we are developing the perturbative expansion around the ultra-local model, where fields defined in different points of the Euclidean space are decoupled. We first study the strong-coupling expansion in the $(\lambda\varphi^{4})_{d}$ theory. Assuming the ultra-local approximation, we study the singularities of this perturbative expansion, analysing the analytic structure of the zero-dimensional generating function in the complex coupling constant plane. Second, we discuss the ultra-local generating functional in two idealized field theory models defined by the following interaction Lagrangians: ${\cal{L}_{II}} (g_{1},g_{2};\varphi)=g_{1}\varphi^{\,p}(x)+g_{2}\varphi^{-p}(x)$, and the sinh-Gordon model, i.e., ${\cal{L}_{III}}(g_{3},g_{4};\,\varphi)= g_{3}\left(\cosh (g_{4}\,\varphi(x))-1\right)$. To control the divergences of the strong-coupling perturbative expansion two different steps are used through the paper. First we introduce a lattice structure only to give a meaning to the ultra-local generating functional. On the other hand, the resulting perturbative expansion is an expansion for the continuum and not for the lattice approximation. Thus, using an analytic regularization procedure we discuss briefly how it is possible to obtain a renormalized Schwinger functional associated with these models, going beyond the ultra-local approximation withouth using a lattice regularization procedure.
- Ano
- 2003
- Número
- CBPF-NF-014/03
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não